In France it would be yes and no.

Access to health care, school, unofficial job, yes.
Buy a house, I do not know, I would say no, but I may be wrong (at least not from the legal market that requires a bank account, a lawyer for papers...).

Immigration politics has been tighter in the last years. And promises made by the new Super-Prez to make them even tighter.
Last year though, a large number of illegal immigrants were made legal. Based on kids born in France, going to school, the whole family speaking french, some kind of a job (even illegal), wishes to integrate within the french society (there was an interview).

The social mesh is pretty extensive here, directed for years towards helping and protecting the weakest persons, the youth, the elders, etc.
That may change.